https://file.aiquickdraw.com/mathbot/file/1730434819649b4msmfbd.jpg

To solve this problem, we need to determine the number of prime numbers in each specified interval. Here's how we can find these values:

1. **Interval 0 to 40**:
   We count the primes between 0 and 40:  
   \( 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37 \).  
   **There are 12 primes in this range.**

2. **Interval 40 to 80**:
   Primes between 40 and 80 are:  
   \( 41, 43, 47, 53, 59, 61, 67, 71, 73, 79 \).  
   **There are 10 primes in this range.**

3. **Interval 80 to 120**:
   Primes between 80 and 120 are:  
   \( 83, 89, 97, 101, 103, 107, 109, 113 \).  
   **There are 8 primes in this range.**

4. **Interval 120 to 160**:
   This interval was provided with the correct answer of **7** primes.

5. **Interval 160 to 200**:
   Primes between 160 and 200 are:  
   \( 163, 167, 173, 179, 181, 191, 193, 197, 199 \).  
   **There are 9 primes in this range.**

### Summary of Answers
- **0 to 40:** 12
- **40 to 80:** 10
- **80 to 120:** 8
- **120 to 160:** 7 (already correct)
- **160 to 200:** 9

Let me know if you'd like further details on any of the calculations, or if you have other questions. 

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### Related Questions
1. How are prime numbers distributed in other intervals, like 200 to 300?
2. What methods can help efficiently find the number of primes in large intervals?
3. How do we prove there are infinitely many prime numbers?
4. What are some patterns observed in prime numbers across different ranges?
5. Can prime number density be approximated in any range using a formula?

### Tip
A useful tool for finding prime numbers in a range is the **Sieve of Eratosthenes** algorithm, which efficiently finds all primes up to a given limit.

The number of primes in each interval: 0-40, 40-80, 80-120, 120-160, and 160-200.

Discover how to find the number of prime numbers in specified intervals from 0 to 200. This problem applies concepts from number theory, including the infinitude of primes, to identify prime counts within intervals. Ideal for high school students studying advanced math.

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